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Constructing a unitary Hessenberg matrix from spectral data (November 1988)

Author: Gragg, William B.;Ammar, Gregory S.;Reichel, Lother.
Subject: ALGORITHMS.; EIGENVALUES.; NUMERICAL ANALYSIS.; PERTURBATIONS.; SPECTRA.
Publisher: Monterey, California : Naval Postgraduate School
Language: en_US
Call number: ocn640932689
Digitizing sponsor: Naval Postgraduate School, Dudley Knox Library
Book contributor: Naval Postgraduate School, Dudley Knox Library
Collection: navalpostgraduateschoollibrary; fedlink; americana
Notes: some content may be lost due to the binding of the book.

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Title from cover

"NPS-53-89-005."

"November 1988."

AD A204 114

Includes bibliographical references (p. 7)

We consider the numerical construction of a unitary Hessenberg matrix from spectral data using an inverse QR algorithm. Any unitary upper Hessenberg matrix H with nonnegative subdiagonal elements can be represented by 2n - 1 real parameters. This representation, which we refer to as the Schur parameterization of H, facilitates the development of efficient algorithms for this class of matrices. We show that a unitary upper Hessenberg matrix H with positive subdiagonal elements is determined by its eigenvalues and the eigenvalues of a rank-one unitary perturbation of H. The eigenvalues of the perturbation strictly interlace the eigenvalues of H on the unit circle. Inverse eigenvalue problem, Unitary matrix, Orthogonal polynomial

aq/aq cc:9116 04/23/99

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